Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(0);
  long long n, flag = 1, c, d, e;
  cin >> n;
  long long j = sqrt(n);
  for (long long i = 1; i <= j; i++) {
    c = (i * (i + 1));
    d = sqrt((2 * n) - c);
    e = d * (d + 1);
    if ((c + e) == 2 * n) {
      flag = 0;
      break;
    }
  }
  if (flag == 0 && n != 1) {
    cout << "YES\n";
  } else {
    cout << "NO\n";
  }
  return 0;
}